Interferometric optical techniques are widely used to measure optical thickness, flatness, and other geometric and refractive index properties of precision optical components such as glass substrates used in lithographic photomasks.
For example, one can use an interferometer to combine a test wavefront reflected from a test surface with a reference wavefront reflected from a reference surface to form an optical interference pattern. Spatial variations in the intensity profile of the optical interference pattern correspond to phase differences between the combined test and reference wavefronts caused by, for example, variations in the profile of the test surface relative to the reference surface.
Phase-shifting interferometry (PSI) can be used to accurately determine the phase differences and the corresponding profile of the measurement surface based on a series of optical interference patterns recorded for each of multiple phase-shifts between the test and reference wavefronts. For each spatial location of the pattern, the series of optical interference patterns define a series of intensity values, herein also referred to as interference signal, which depend on the phase difference between the combined test and reference wavefronts for that spatial location. Using numerical techniques known in the art, the phase difference can be extracted from the interference signal for each spatial location. These phase differences can be used to determine information about the test surface including, for example, a profile of the measurement surface relative the reference surface. Such numerical techniques are referred to as phase-shifting algorithms.
In PSI, one distinguishes between linearly varying and sinusoidally varying the relative phase shift between the test wavefront and the reference wavefront.
In sinusoidal PSI, a time dependent phase shift, which varies sinusoidally in time, is introduced between the test light and the measurement light. For each spatial location of the pattern, the interference signal made up of a series of intensity values has a complicated, non-sinusoidal dependence on the phase-shifts. Specifically designed sinusoidal phase-shifting algorithms extract the phase difference for each spatial location from this complicated dependence of the intensity values.
Sinusoidal PSI is described, for example, in commonly owned U.S. Patent Application published as US-2008/0180679-A1 to P. J. De Groot entitled “SINUSOIDAL PHASE SHIFTING INTERFEROMETRY,” the contents of which are herein incorporated by reference. The error compensation and algorithm design procedures disclosed in U.S. Patent Application 2008/0180679 cover random noise, additive noise, multiplicative noise, laser diode intensity modulation, detector nonlinearity, vibrations, calibration error, timing error, phase shift nonlinearity, and sensitivity to frame integration time.
In linear PSI, a time dependent phase shift, which varies linearly in time, is introduced between the test and reference wavefronts. The series of optical interference patterns usually spans a full cycle of optical interference (e.g., from constructive, to destructive, and back to constructive interference). In linear PSI, the interference signal has a sinusoidal dependence on the phase-shifts with a phase difference equal to the phase difference between the combined test and reference wavefronts for that spatial location. Specifically designed linear phase-shifting algorithms extract the phase difference for each spatial location from the sinusoidal dependence of the intensity values.
The varying phase-shifts in sinusoidal and linear PSI can, for example, be produced by various ways that change the optical path length from the test surface to the interferometer relative to the optical path length from the reference surface to the interferometer. For example, the reference surface can be moved (e.g., sinusoidal or linear) relative to the test surface or a modulator may be placed in one of the beam paths. Alternatively, the phase-shifts can be introduced for a constant, non-zero optical path difference by changing the wavelength of the test and reference wavefronts. The latter application is known as wavelength tuning PSI and is described, e.g., in U.S. Pat. No. 4,594,003 to G. E. Sommargren. The ability of certain types of modulating means (e.g., piezoelectric transducers, wavelength tunable lasers, etc) to produce a linear phase shift may be limited, due to, for example, bandwidth limitations.
The interference pattern in a PSI system is typically detected by a conventional camera system, converted to electronic data, and read out to a computer for analysis. In such applications, the optical interference pattern is imaged onto an array of pixels. Charge accumulates at each pixel at a rate that depends on the intensity of the incident light. The charge value at each pixel is then read out, or transferred to a data processing unit. The charge values for a series of phase-shifts form the interference signal of that specific pixel.